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Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3.1 department of mathematics,east {3. university of Science and Technology,shanghai 20023.,{3. 2 department of mathematics,Anhui Normal university,Wuhu 241000,{3. 3.department of mathematics,Donghua university,shanghai 201620,{3. 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching

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Science china mathematics 2011年第3期54卷 603-610页

作者： wang PeiHe1 & WEN YuLiang2 1School of Mathematical Sciences, Qufu Normal university, Qufu 273.65, china 2{3. of mathematics, east china Normal university, shanghai 200241, china 1. School of Mathematical Sciences Qufu Normal University Qufu 273165 China2. Department of Mathematics East China Normal University Shanghai 200241 China

Let Mn be a compact, simply connected n (≥3.-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.

关键词： k-th Ricci curvature Hausdorff convergence differentiable sphere theorem harmonic coordinate harmonic radius

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science china mathematics 2010年第3期53卷 719-738页

作者： KONG DeXing 1 , LIU KeFeng 2 & wang YuZhu 3. 1 department of mathematics, Zhejiang {3., Hangzhou 3.0027, china 2 department of mathematics, {3. of California at Los Angeles, CA 90095, USA 3.department of mathematics, shanghai Jiao Tong {3., shanghai 200248, china 1. department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Department of Mathematics Shanghai Jiao Tong University Shanghai 200248 China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition Cauchy problem smooth solution

SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

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Chinese Annals of mathematics,Series B 2005年第4期26卷 651-658页

作者： wang MENG department of mathematics, Zhejiang {3., Hangzhou 3.0027, china School of Mathematical Sciences, Pudan {3., shanghai 20043., china. department of mathematics Zhejiang University Hangzhou 310027 China. School of Mathematical Sciences Fudan University Shanghai 200433 China

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(... 详细信息

关键词： Sobolev inequality Complete manifold Riesz transform Potential Heat kernel

Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： wang Hanxing 1 and DAI Yonglong 2 1. department of mathematics, {3. university, {3. 201800, china 2. department of mathematics, Zhongshan university, Guangzhou 510275, china department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Construct non-graded bi-Frobenius algebras via quivers

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Science china mathematics 2007年第3期50卷 450-456页

作者： Yan-hua wang & Xiao-wu CHEN department of Applied mathematics, {3. university of Finance and Economics, {3. 20043., china department of mathematics, university of Science and Technology of china, Hefei 23.026, china department of Applied mathematics Shanghai University of Finance andEconomics Shanghai 200433 China

Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.

关键词： quivers bi-Frobenius algebras graded algebras 16W3. 16G20

The pricing of perpetual convertible bond with credit risk

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Applied mathematics(A Journal of Chinese Universities) 2010年第3期25卷 277-290页

作者： wang Le-le BIAN Bao-jun department of mathematics, Tongji {3., shanghai 200092, china department of mathematics Tongji University Shanghai China

Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.

关键词： Convertible bond default risk optimal stopping problem variational inequality free boundary.

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of mathematics East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value

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Acta Mathematica Sinica,English Series 2001年第2期17卷 197-206页

作者： Yuan Di wang department of mathematics, {3. university, {3. 20043.. P. R. china department of mathematics Shanghai University Shanghai 200436 P. R. China

Recently much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDE with linear homogeneous boundary conditions, and to other ones with nonlinear boundary conditions, provided the ordered upper and lower solutions are given. Semigroup, fractional order function spaces and generalized Poincare operators play an important role in proving the existence of solutions.

关键词： Nonlocal problem Nonlinear boundary condition Palabolic equation Solution Existence Generalized Poincaree operator